Summary: An efficient, straightforward method for obtaining a multi-component integrable hierarchy and the multi-component integrable coupling system is proposed in this paper. A new 4M-dimensional loop algebra \(\widetilde X\) is constructed firstly, whose commutation operations defined by us are as simple and straightforward as that in the loop algebra \(\widetilde {A_1}\). As an application example, a new isospectral problem is established, then the well-known multi-component Schrödinger hierarchy and the multi-component mKdV hierarchy are obtained. So we call it the multi-component S-mKdV hierarchy. Finally, an expanding loop algebra \(\widetilde{F}_M\) of the loop algebra \(\widetilde X\) is presented. Based on the \(\widetilde{F}_M\), the multi-component integrable coupling system of the multi-component S-mKdV hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.